Topological solutions

该奖项由2009年美国复苏和再投资法案(公法111-5)资助。PI研究作为Seifert猜想和修正的Seifert猜想的反例的拓扑动力系统和叶层中极小集的结构。这些极小集的有趣性质是拓扑维、Hausdorff维、孤立性和与形理论相关的捷克同调。动力学也被用在离散几何和计算几何的工作中。动力学系统影响科学的其他领域。极小集的研究是不动点和吸引子研究的扩展。除了传统的科学技术工程和数学(STEM)领域外，该理论还适用于生物学、人口研究和经济。PI研究的几何问题在医学成像中有应用。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The PI investigates the structure of minimal sets in topological dynamical systems and foliations that serve as counterexamples to the Seifert Conjecture and the Modified Seifert Conjecture. The interesting properties of these minimal sets are the topological dimension, the Hausdorff dimension, isolation, and Czech homology in relation to shape theory. Dynamics is also employed in work on problems in discrete and computational geometry.Dynamical systems impact other areas of science. The study of minimal sets is an extension of the study of fixed points and attractors. The theory has application to biology, population research, and economy, in addition to the traditional Science Technology Engineering and Mathematics (STEM) fields. The geometry problems studied by the PI have applications to medical imaging.